1. Field of the Invention
This invention relates to a system and method for automatically dividing a form of an object to be analyzed (analysis object) into areas, for example, when a finite element method is applied for conducting various analyses of the object.
2. Description of the Related Art
Heretofore, various methods have been developed for an automatic mesh generation method for the finite element method, a technique of dividing the object into areas and conducting various analyses, such as a structure analysis and an electromagnetic field analysis.
Various methods, such as a fuzzy inference application method, a mapping technique application method, a method of section, and an adaptive method have been proposed; the methods are described in documents such as "Feb. 22, 1993, issue of Nikkei Mechanical, pp.52-59."
An area division method of the analysis object form using an expert system has also been developed; it is described in documents such as "K. Reichert et al.: AUTOMATIC MESH GENERATION BASED ON EXPERT-SYSTEM-METHODS, IEEE TRANSACTIONS ON MAGNETICS, VOL.27, NO.5, pp.4197-4200, SEP. 1991."
On the other hand, the genetic algorithm applied in the invention is an algorithm whose idea is conceived from the principles relating to the evolution of living things. It is a technique for learning, optimization, etc., using a probabilistic search; it is described in documents such as "Goldberg, D. E., GENETIC ALGORITHM in Search, Optimization, and Machine Learning, Addison Wesley, 1989," "GENETIC ALGORITHM, compiled by Hiroaki KITANO, Sangyo Tosho, First Edition on Jun. 3, 1993," and "Autumn Issue of Nikkei Al, pp.106-111, 1991."
By the way, in the fuzzy inference application method of the automatic mesh generation method in the related art as described above, basically triangle elements are generated on a two-dimensional plane. Thus, division of a three-dimensional form results in three-dimensional elements of tetrahedrons and it is difficult to generate three-dimensional elements having a hexahedron form at present.
In the mapping technique application method, the form of the analysis object is converted into a rectangular coordinate system and is divided into rectangular parallelopipeds, then the results are further subjected to inverse coordinate conversion for restoring to the original form. Thus, the forms of the objects to which the method is applicable are limited and it is difficult to perform flexible element division.
The method of section, which is a semi-automatic method, requires that the user should prepare so-called section generation axes. Further, the adaptive method repeats, more than once, a process in which initial meshes are generated, then an actual numerical analysis is made and meshes are regenerated based on the analysis result, and then a numerical analysis is made. Thus, costs required for calculation of division processing increase and if the initial meshes are not properly generated, analysis precision lowers remarkably.
Further, the mesh generation method using an expert system mentioned above is means for generating triangle elements at poor analysis precision.
On the other hand, when meshes generated by an actual analyst (user) are observed, he or she divides the object into fine meshes in a portion to be analyzed at high precision and rough meshes in other portions, based on his or her experiential knowledge for satisfying both the conditions of ensuring good analysis precision and reduction of costs required for calculation of division processing.
If the form of an object is given, the mesh generation state is not uniquely determined and various division forms into meshes generated by analysts for a single analysis object are possible. This means that the degree of freedom of the element division is high and the number of division method combinations becomes enormous in the mesh generation process.
The genetic algorithm is proposed as an effective method for solving a combinatorial optimization problem. In the algorithm for simulating the evolutionary process of living things, such as the generation of an initial group, evaluation of environment adaptability, selection, crossover, and mutation, determination of specific gene and chromosome structures, an environment adaptability evaluation method, and a processing method of selection, crossover, mutation, etc., dependent on the gene and chromosome structures are important problems to be considered when adopting the genetic algorithm.